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I keep trying, but I can't get this.

 

The two solutions of the equation x^2 + bx + 18 = 0 are in the ratio of 3 to 1 for some values of b.  What is the largest possible value of b?

 Nov 27, 2022
 #1
avatar+115 
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Hm.. can you explain further for the 3:1 ratio is it for the variable b or the variable x?

 Nov 27, 2022
 #2
avatar+115 
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I get it now. Okay so first, look at the constant term 18. we need some 2 numbers to be in a 3:1 ratio and multiply to get 18 so

\(xy=18\)

\(4y=x\)

from this system of equations we get

\(y = \sqrt{4.5}\)

\(x = \sqrt{72}\)

these are the 2 solutions the this quadratic.

we can express this as

\((x - \sqrt{4.5})(x-\sqrt{72}) = 0\)

so b is equal to \(\sqrt{4.5} + \sqrt{72}\)

hope this helped(i hope this is not wrong)

 Nov 27, 2022

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